docs: tighten MVP test guide

Make the manual MVP proof easier to run without adding product fluff. Add a
short fast path, explicit log-capture commands, the expected release binary
paths, an extra Windows route-table check, and the relay-route pin disposition
to the report-back checklist.

The test guide remains centered on the real acceptance criteria: DHCP over the
TAP tunnel, TAP-sourced ping to a LAN host, switch MAC learning on the gateway
port, LAN-game discovery or join, and a gateway restart sanity check.

Test Plan:
- git diff --check
- git diff --cached --check

Refs: MVP E2E handoff

TESTING.md

@@ -9,6 +9,19 @@ Windows TAP client -> public QUIC relay -> Linux AF_PACKET gateway -> LAN
 The MVP is intentionally manual. It does not include an installer, GUI,
 production certificates, auth, or end-to-end payload encryption.
 
+## Fast Path
+
+Run the test in this order:
+
+1. Build the relay and gateway on Linux, and build the Windows client on
+   Windows.
+2. Start the relay and keep `relay-cert.der`.
+3. Copy `relay-cert.der` to the gateway and Windows client.
+4. Start the Linux gateway on the wired LAN interface.
+5. Start the Windows client from an elevated terminal.
+6. Verify DHCP, `ping -S`, switch MAC learning, and one LAN game.
+7. Restart the gateway once while the client stays up.
+
 ## MVP Pass Conditions
 
 The MVP proof is successful when all of these are true:
@@ -48,6 +61,25 @@ Windows TAP IPv4:
 Use the same room code everywhere, for example `ROOM1`.
 Start order is relay first, gateway second, Windows client last.
 
+## Log Capture
+
+Keep one log per process. They are the easiest way to diagnose a failed run.
+
+On Linux:
+
+```bash
+./target/release/lanparty-relay ... 2>&1 | tee relay.log
+sudo ./target/release/lanparty-gateway ... 2>&1 | tee gateway.log
+```
+
+On Windows PowerShell:
+
+```powershell
+Start-Transcript .\client.log
+.\target\release\lanparty-client-win.exe ...
+Stop-Transcript
+```
+
 ## Build Prerequisites
 
 On Windows, use the Rust MSVC toolchain and install Visual Studio Build Tools
@@ -79,6 +111,14 @@ On Windows, in an Administrator terminal:
 cargo build --release -p lanparty-client-win
 ```
 
+The binaries used below are:
+
+```text
+Linux:   ./target/release/lanparty-relay
+Linux:   ./target/release/lanparty-gateway
+Windows: .\target\release\lanparty-client-win.exe
+```
+
 The Windows client must run elevated because it opens TAP and edits routes.
 The gateway usually needs root because it opens an AF_PACKET raw socket.
 
@@ -214,6 +254,7 @@ Connected to LAN gateway
 
 ```powershell
 Get-NetIPAddress | ? InterfaceAlias -like "*TAP*"
+Get-NetRoute | ? InterfaceAlias -like "*TAP*" | ft -AutoSize
 ```
 
 Use the non-link-local IPv4 address as `<tap-ip>` in the next step.
@@ -395,3 +436,4 @@ For a useful test report, capture:
 - switch MAC-table entry for the Windows client MAC
 - LAN game discovery or join result
 - lifecycle sanity-check result
+- whether the relay route pin was `(created)` or `(already existed)`